I have hard time envisioning how they would move. 3, 4 and 6 almost look like different stages of the same helixoid.
On close inspection you can see that they have been drawn with one line that has a beginning and an end.
Which gives me an idea for one option of how to animate it: Draw one complete helix shape as a mask and then use generate>stroke to draw it, animating the beginning and end values. To make it seamless, you will have to use two strokes, as you can only go from 0 to 100% on the completeness of the stroke.
AE project to demonstrate the idea at below link.
9042_helixdraw.aep.zip
I drew just one loop, but you get the idea.